NEET Physics — Electrostatic Potential and Capacitance

Two charges \( 8 \, \mu\text{C} \) and \( -4 \, \mu\text{C} \) are at \( (6, 0, 0) \) and \( (-6, 0, 0) \, \text{cm} \). What is the potential at midpoint? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Two charges \( 10 \, \mu\text{C} \) and \( -5 \, \mu\text{C} \) are placed 20 cm apart. What is the potential energy of the system? (Take \( \frac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \, \text{Nm}^2 \text{C}^{-2} \)).

Why does the capacitance of a parallel plate capacitor increase when a dielectric slab is inserted between the plates while keeping the plates connected to a battery?

A metal sphere is placed inside a uniform electric field \( E \). What is the electric field inside the sphere after it reaches electrostatic equilibrium?

A parallel plate capacitor has plates of area \( 0.02 \, \text{m}^2 \) separated by 2 mm in air. What is its capacitance? (Take \( \varepsilon_0 = 8.85 \times 10^{-12} \, \text{C}^2 \text{N}^{-1} \text{m}^{-2} \)).